Find the 15th term of the series $\sqrt{3} + \dfrac{1}{\sqrt{3}} + \dfrac{1}{3\sqrt{3}} + ….$

The given list of numbers,

$\sqrt{3} + \dfrac{1}{\sqrt{3}} + \dfrac{1}{3\sqrt{3}} + ….$ is a G.P. with first term a = $\sqrt{3}$ and common ratio = r = $\dfrac{1}{3}.$

By formula, a_n = ar^{n - 1}

∴ a₁₅ = $\sqrt{3}\Big(\dfrac{1}{3}\Big)^{14} = 3^{1/2}\Big(\dfrac{1}{3^{14}}\Big) = 3^{1/2}\times 3^{-14} = 3^{1/2 - 14} = 3^{-27/2} .$

Hence, the 15th term of the G.P. is $3^{-27/2}$.